ArcGIS will manage your Results Tab for you from Geoprocessing > Geoprocessing Options > Results Management. However, Field Calculator may result in MXD bloat before the application deletes the results for you (default is two weeks). You can manually delete the results in ArcMap > Results Tab > Previous Sessions. Right click on the Results tree items > Delete All. This will permamntly delete your GP results, so make a back up of the MXD if you think you may want them.